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regular language

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Let

$L_1=\{a^p \; \mid \; \text{p is prime}\}$, and $L_2=\{a^nb^m \; \mid \; m,n\geq 0\}$

then  $L_1.L_2=\{a^ib^j \; \mid \; i\geq 2,j\geq 0\}$ is Regular.

and $L_2.L_1=\{a^ib^ja^p \; \mid \; i,j\geq 0,\text{p is prime}\}$ is Non-regular.

So both statement are false. 

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